Algebra question where the "x" appears twice

Not sure what this kind of question is called, but here it is:

x10 + (1-x)11 = 10.8

find x.

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I know x = 0.2 but the only way I can find it is with trial and error.\

I have tried shifting terms around but I can not seem to combine the two x's to get a final answer.

If anyone could write out the steps for solving this that would be great :)

You can rearrange it to: 10x + 11(1-x) = 10.8 if you want, I have written it differently for a specific reason but it is not important for solving the question.

Once again, I can find the answer with trial and error but I don't have time for that in the exam :O

Thanks in advanced!